Post on 11-Jan-2016
description
Large SOLID TARGETS
for a Neutrino Factory
J. R. J. Bennett
Rutherford Appleton Laboratory
roger.bennett@rl.ac.uk
Note.
•In all cases I will refer to the power in the target rather than the beam.
Thus, in the case of the neutrino factory, a 1 MW target has 1 MW dissipation and the beam power is 4 MW.
•I will not talk about liquid metal targets.
Contents
1. Solid target review -- or
Why are we afraid of solid targets?
2. Proposed R&D in the UK
Typical Schematic Arrangement of a Neutrino Factory Target
targetprotons
Target
Heavy metal - Tantalum
2 cm
20 cm
Beam hits the whole target
Not a stopping target
SOLID Targets
Need to remove the heat - 1 MW
BUT
The PERCIEVED problem is
SHOCK WAVES
Shock
Shock processes are encountered when material bodies are subjected to rapid impulse loading, whose time of load application is short compared to the time for the body to respond inertially.
R A Graham in High-Pressure Shock Compression of Solids. Ed. J R Asay & M Shahinpoor, Springer-Verlag, 1992
The processes are all non linear so mathematical description is complex. Further, discontinuities complicate solution. Thus specialised techniques have been constructed to render the problem mathematically tractable.
Neil Bourne, RMCS, Shrivenhamprivate communication
Examples of Shock Events:
•Explosions
•Bullets Impacting
•Volcanic Eruptions
•Meteor Collisions
•Aircraft Sonic Boom
Simple explanation of shock waves
inertia prevents the target from expanding until:
the temperature rises by ΔT and the target expands by Δd (axially)
target
Short pulse of protons
Short pulse of protons
Time
t = 0
2d
t > 0
v is the velocity of sound in the target material; is the coefficient of linear expansion
End velocity
Δd
d v t
vTd
vd
t
dV
End velocity
vC
qvT
d
vd
t
dV
Where:
v is the velocity of sound in the target material
is the coefficient of linear expansion
q is the energy density dissipated (J g-1)
C is the specific heat (J g-1)
The velocity of sound is given by,
E
v
where E is the modulus of elasticity and the density
Thus the end velocity becomes,
E
C
qV
To minimise V, for a given q, select a material with:
small; C & large. (Super-Invar has a very small but losses this property under irradiation)
E
C
eE
C
qV
Expressing the energy density in terms of J cm-3,
Hence the momentum of the end of the target can be found.
Since the force is equal to the rate of change of momentum it is possible to calculate the stress in the material.
In the case of the Neutrino factory target the stress exceeds the strength – disaster.•Can make a better analysis - Peter Sievers, under ideal elastic conditions, CERN Note LAB.II/BT/74-2, 1974.•There are modern stress analysis packages available commercially to deal with dynamic situations.•Chris Densham has calculated (ANSYS) that a solid tantalum target for the neutrino factory will probably show signs of shock fracture after a few pulses.
Shock, Pulse Length and Target Size
If we heat a target uniformly and slowly – there is no shock!
Or,
when the pulse length is long compared to the time t taken for the wave to travel across the target – no shock effect!
So,
if we make the target small compared to the pulse length there is no shock problem.
If No problem!
Assume = 2 s, V = 3.3x105 cm s-1 , then d = 0.7 cm
Also need sufficient pulsed energy input.
V
dt
This principle has been used in the target designed by Peter Seivers (CERN).
Solid Metal Spheres in Flowing Coolant •Small spheres (2 mm dia.) of heavy metal are cooled by the flowing water, liquid metal or helium gas coolant.•The small spheres can be shown not to suffer from shock stress (pulses longer than ~3 s) and therefore be mechanically stable.
Looks like we have a problem for large targets!
(2 cm diameter, 20 cm long)
BUT!
Have we seen shock wave damage in solid
targets?
What do we know?
There are a few pulsed (~1s) high power density
targets in existence:Pbar – FNALNuMISLAC (electrons)
Table comparing some high power pulsed proton targetsFacility Particle Rep. Power Energy Energy Life Number
Rate /pulse density of pulses/pulse
f P Q height width length volume thick material q N
Hz W J cm cm cm cm3 cm J cm-3 days
NuFact protons 50 1E+06 20000 2 2 20 63 20 Ta 318 279 1.E+09Number of pulses on any one section of the toroid 7.E+06
ISOLDE protons 1 3675 0.6 1.4 20 13 0.05 to Ta 279 21 2.E+060.0002
ISIS protons 50 180000 3600 7 7 30 1155 0.7 Ta 3 450 2.E+09
Pbar protons 0.3 1797 0.19 0.19 7 0.25 ~6 Ni 7112 186 5.E+06 Run I 3E12 ppp (Cu, SS, Inconel) Damage
Run II 5.E+12 Damage in one or a few pulses 13335
Future 1.E+13 0.15 0.15 30000
NuMI protons 0.53 0.1 0.1 95 2 C 600
120 GeV Radiation Damage - No visible damage at 2.3E20 p/cm2
4E13 ppp Shock - no problem up to 0.4 MW (4E13 at 1 Hz)8.6 s Sublimation -OK
Reactor tests show disintegration of graphite at 2E22 n/cm2
NuMI will receive a max of 5E21 p/cm2/year
Beam and Target size
Facility Particle Rep. Power Energy Energy Life Number Rate /pulse density of pulses
/pulsef P Q height width length volume thick material q N
Hz W J cm cm cm cm3 cm J cm-3 days
NuFact protons 50 1E+06 20000 2 2 20 63 20 Ta 318 279 1.E+09Number of pulses on any one section of the toroid 7.E+06
SLC e 120 5.E+03 42 0.08 0.08 2 W/Re 591 1500 6.E+05SLAC 33 GeV Rotating disc, 6.35 cm diameter, 2cm thick 26% Re
Target designed to withstand shock
Radiation damage leading to loss of strength and failure when subjected to shock
FXR e Ta 160 100LLNL 17 MeV Ta 267 10
No damage
RAL/TWI e 100 4.E+04 0.2 25 m Ta 500 up to 1E+06150 keV Thin foil 0.4 cm wide Range ~10 m
Failures probably due to oxidation in poor vacuum
Beam and Target size
Table comparing some high power pulsed electron targets
No damage with ISOLDE (foil) or ISIS targets; but some damage with Pbar targets.In 2 tests on solid tantalum bars (20 cm long 1 cm diameter) at ISOLDE Jacques Lettry has observed severe distortion. He considers this is due to shock.
Gas cooling between discs
Stack of slowly rotating discs
proton beam
pbar target
Schematic Diagram of the Pbar target
Section through the pbar target assembly
Vinod Bharadwaj / Jim Morgan
Pba
r T
arge
t (J
im M
orga
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nick
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alum
iniu
m
rhen
ium
copp
er
copp
er
copp
er
cool
ing
disc
s
Ent
ry D
amag
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im M
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Exi
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Proposed R&D in the UK1.Radiation cooled rotating toroid
a) Calcuate levitation drive and stabilisation system
b) Build a model of the levitation system
2.Individual bars
a) Calculate mechanics of the system
b) Model system
3.Calculate the energy deposition, radio-activity for the target, solenoid magnet and beam dump.
Calculate the pion production (using results from HARP experiment) and calculate trajectories through the solenoid magnet.
Proposed R&D, Continued
4. Model the shocka) Measure properties of tantalum at 2300 K
b) Model using hydrocodes developed for explosive applications at LANL, LLNL,
AWE etc.c) Model using dynamic codes developed by
ANSYS5. Continue electron beam tests on thin foils,
improving the vacuum6. In-beam test at ISOLDE - 106 pulses 7. In-beam tests at ISIS – 109 pulses
Plan View of Targetry SetupPlan View of Targetry Setup
shielding
rollersAccess
port
rollers
rollers
protonsto dump
cooling
coolingcooling
solenoid channel
1 m water pipes
x
z
Bruce King et al
Schematic diagram of the rotating toroidal target
rotating toroid
proton beam
solenoid magnet
toroid at 2300 K radiates heat to water-cooled surroundings
toroid magnetically levitated and driven by linear motors
Heat Dissipation
by
Thermal Radiation
This is very effective at high temperatures due to the T4 relationship
POWER DISSIPATION
0.01 0.1 1 10 100 1 103
0.01
0.1
1
10
100
1 103
power
MW10 m
10 m
v = 100 m/s
1 m
1 m
100 m
100 m
0.1 m
200 m
20 m10 m
2 m
0.1 m
1 m
2000 m
1000 m
radius/velocity
v = 20 m/s
v = 10 m/s
v = 1 m/s
v = 0.1 m/s
1000 m
10 m
100 m
10000 m
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 1 104
0.01
0.1
1
10
100
1 103
1 104
T, K
velocity, (V = l f), cm/s
PowerMW
1
36
10
0.1
Temperature Rise v Velocity at Different Powers
50Hz
100 Hz
for l = 20 cm
Target Designs
1.Toroid
If the toroid breaks there are problems.
Individual bars are better
2. Bars on a wheel
- Problems with the solenoid magnet
3. Free bars
drive shaft
protons
spoke
solenoid coils
vacuum box
target
Wheel Target
1MW Target Dissipation (4 MW proton beam)
tantalum or carbon radiation cooled temperature rise 100 K speed 5.5 m/s (50 Hz) diameter 11 m
solenoid
collection and cooling reservoir
proton beam
Individual free targets
Levitated target bars are projected through the solenoid and guided to and from the holding reservoir where they are allowed to cool.
Individual Targets
suspended from a
Guide Wire
VV = Lf
R governed by power
Threading solenoid
Choice of Target Material
Tantalum
Why?
Why Tantalum?
1.Refractory. Melting point 3272 K
2.Good irradiation properties
No damage observed with ISIS tantalum target after bombardment with 1.27x1021 protons/cm2, suffered 11 dpa. No swelling. Increased yield strength. No cracking. Remains very ductile. Hardness increased by a factor <2. [J. Chen et al, J. Nucl. Mat. 298 248-254 (2001)]
3. Relatively easy to machine and weld etc.